Deformations of asymptotically cylindrical G2-manifolds

Johannes Nordström

doi:10.1017/S0305004108001333

Deformations of asymptotically cylindrical G₂-manifolds

Johannes Nordström

Department of Mathematical Sciences

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14 Citations (SciVal)

Abstract

We prove that for a 7-dimensional manifold M with cylindrical ends the moduli space of exponentially asymptotically cylindrical torsion-free G₂-structures is a smooth manifold (if non-empty), and study some of its local properties. We also show that the holonomy of the induced metric of an exponentially asymptotically cylindrical G₂-manifold is exactly G₂ if and only if the fundamental group π₁(M) is finite and neither M nor any double cover of M is homeomorphic to a cylinder.

Original language	English
Pages (from-to)	311-348
Number of pages	38
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	145
Issue number	2
Early online date	19 May 2008
DOIs	https://doi.org/10.1017/S0305004108001333
Publication status	Published - 1 Sept 2008

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AB - We prove that for a 7-dimensional manifold M with cylindrical ends the moduli space of exponentially asymptotically cylindrical torsion-free G2-structures is a smooth manifold (if non-empty), and study some of its local properties. We also show that the holonomy of the induced metric of an exponentially asymptotically cylindrical G2-manifold is exactly G2 if and only if the fundamental group π1(M) is finite and neither M nor any double cover of M is homeomorphic to a cylinder.

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Deformations of asymptotically cylindrical G₂-manifolds

Abstract

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